Apply the quotient rule, which is:
dxdg(x)f(x)=g2(x)−f(x)dxdg(x)+g(x)dxdf(x)
f(x)=x and g(x)=(x−1)2.
To find dxdf(x):
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Apply the power rule: x goes to 1
To find dxdg(x):
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Let u=x−1.
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Apply the power rule: u2 goes to 2u
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Then, apply the chain rule. Multiply by dxd(x−1):
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Differentiate x−1 term by term:
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The derivative of the constant −1 is zero.
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Apply the power rule: x goes to 1
The result is: 1
The result of the chain rule is:
Now plug in to the quotient rule:
(x−1)4−x(2x−2)+(x−1)2